Advanced topics in gauge theory: mathematics and physics of Higgs bundles

Abstract

These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for Advanced Study. We begin by introducing Higgs bundles and their main properties (Lecture 1), and then we discuss the Hitchin fibration and its different uses (Lecture 2). The second half of the course is dedicated to studying different types of subspaces (branes) of the moduli space of complex Higgs bundles, their appearances in terms of flat connections and representations (Lecture 3), as well as correspondences between them (Lecture 4).

References in corpus (6)

• Homological stability for moduli spaces of high dimensional manifolds. I
• Homological stability for moduli spaces of high dimensional manifolds
• On the infinite loop space structure of the cobordism category
• Homological Stability for Diffeomorphism Groups of High Dimensional Handlebodies
• Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n+1
• Invertible Topological Field Theories

Cited by in corpus (2)

• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• On the ${\Delta }_a$ invariants in non-perturbative complex Chern-Simons theory